Ramp Jump Attitude Control of Single-Track Two-Wheeled Robot via Contact-Implicit Trajectory Optimization

In contrast to attitude control strategies relying solely on the aerial phase, the single-track two-wheeled (STTW) robots can adjust their attitude during both the take-off and the aerial phase in the ramp jump task, enabling a wider range of adjustments to achieve an appropriate landing attitude, which introduces a multi-contact problem. In this paper, we leverage recent methods in contact-implicit trajectory optimization (CITO) to handle the multi-modal planning aspect. First, we derive the dynamics of the STTW robot covering the take-off and the aerial phase. Next, two slack variables are introduced to unify the multi-contact constraints, resulting in a contact-implicit model. Then the ramp jump CITO problem is formulated and provides the reference trajectories for attitude angles and actuators. Finally, the effectiveness of the optimization solution is validated through Webots simulations.